As proved in [1]}, \(\mathsf {Ch}_{\mathfrak {m},p}(f)\)  can be represented in terms of the so called minimal weak upper gradient \(|\nabla f|\)  as
\(\mathsf {Ch}_{\mathfrak {m},p}(f)= \frac{1}{p}\int _X |\nabla f|^p\, \mathsf {d}\mathfrak {m}\, .\) 
